Name
Abstract | ||
|---|---|---|
For each nonempty integer partition pi, we define the maximal excludant of pi as the largest nonnegative integer smaller than the largest part of pi that is not itself a part. Let sigma maex(n) be the sum of maximal excludants over all partitions of n. We show that the generating function of sigma maex(n) is closely related to a mock theta function studied by Andrews, Dyson and Hickerson, and Cohen, respectively. Further, we show that, as n -> infinity, sigma maex(n) is asymptotic to the sum of largest parts over all partitions of n. Finally, the expectation of the difference of the largest part and the maximal excludant over all partitions of n is shown to converge to 1 as n -> infinity. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.37236/8736 | ELECTRONIC JOURNAL OF COMBINATORICS |
DocType | Volume | Issue |
Journal | 28 | 3 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shane Chern | 1 | 1 | 1.16 |